基于小世界原理的模型降阶优化研究

Model Reduction Optimization Based on Small-World Principle

为了克服模型降阶问题参数多且易陷入局部最优值的缺点,借鉴社会网络中的小世界原理,提出了基于十进制编码策略的局部短连接和随机长连接搜索算子,进而构造了一种十进制编码的小世界优化算法(DSWA).对稳定和非稳定线性系统的模型降阶优化进行了试验,验证了DSWA算法求解的可行性和有效性.区间固定与区间动态扩展策略的对比结果表明,采用区间动态扩展策略要优于区间固定策略,且DSWA算法能在一定程度上克服陷入局部最优值的问题.此外,通过对比所得优化模型与原始模型之间的误差值、时频域响应曲线等,表明采用DSWA算法得到的降阶模型具有较优的逼近性能.

There are many parameters in model reduction problems and some algorithms are prone to trap in local optimum. Based on the small-world principle in social networks, a decimal-coding local short-connection operator and a random long-connection search operator are proposed. Then a decimal-coding small world algorithm （DSWA） is designed, whose validity and feasibility are testified by the simulation of stable and unstable search-space fixation scheme with expansion scheme, linear system model reduction. Comparing the results indicate that search-space expansion scheme is better than search-space fixation scheme, and DSWA can avoid trapping in local optimum to a certain extent. And a comparison between the optimization model and the original model in the indicators of the error and the time-domain and frequency responses, exhibits the better approximate properties of the reduction model obtained by DSWA.